Because you are improving your fitness, you are bumping up your lactate threshold heart rate and the speed you can produce at threshold. You can do a field test after you’ve recovered from your first race to find your new heart rate training zones.
Using the new training zones, you can follow the last few weeks of the training plan from your first race as you prepare for the second and third races. For example, if you used a 12-week plan and there are five weeks between your recovery and the second race, you can use the last five weeks of the plan. If the third race is three weeks after the second one, use the last three weeks of the plan.
Of course, you can also change to a plan that increases training volumes and training intensities if you prefer.
What if my second race is longer?
If you do a sprint race early in the season, you can bump up to the Olympic distance later in the season. I like some six to nine weeks between the sprint and Olympic races for beginners and those easing back into the sport. Athletes that currently have a good amount of fitness from running or cycling can reduce the time between races, depending on current fitness levels.
No matter whether you do one race or three, make your primary goal to have fun. If you have a great time in the training process, then the races are just celebrations of your fitness.
Search for a triathlon.